Problem: Simplify the following expression: $q = \dfrac{2}{4a + 9} \div \dfrac{10}{5a}$
Solution: Dividing by an expression is the same as multiplying by its inverse. $q = \dfrac{2}{4a + 9} \times \dfrac{5a}{10}$ When multiplying fractions, we multiply the numerators and the denominators. $q = \dfrac{ 2 \times 5a } { (4a + 9) \times 10}$ $q = \dfrac{10a}{40a + 90}$ Simplify: $q = \dfrac{a}{4a + 9}$